Principal parts and paradigm complexity - Center for Computational ...

Gregory Stump University of Kentucky ([email protected])

(Center for Computational Sciences, University of Kentucky, September 19, 2007)

Raphael Finkel University of Kentucky ([email protected])

Principal parts and paradigm complexity

ASSUMPTION: Not all of the forms in a lexeme’s paradigm are necessarily listed lexically. How should the inference of unlisted forms be modelled?

III

Conjugations: II

I

Morphosyntactic property sets: X

! ! ?

Y

Z

TABLE 1. Deducing a class II verb’s Y form in an exponence-based approach

III

Conjugations: II

I

principal -> part

TABLE 2. Deducing a class II verb’s Y form in an implicative approach Morphosyntactic X Y Z property sets:

In the implicative approach, the listed members of a lexeme’s paradigm from which its unlisted members are inferred are its PRINCIPAL PARTS.

TABLE 3. Principal parts of five Latin verbs 1sg 1sg Perf. pass. present perfect participle Conjugation Infinitive Gloss indicative indicative (neut. nom. active active sg.) 1st laudō laudāre laudāvī laudātum ‘praise’ 2nd moneō monēre monuī monitum ‘advise’ 3rd dūcō dūcere dūxī dūctum ‘lead’ 3rd (-iō) capiō capere cēpī captum ‘take’ 4th audiō audīre audīvī audītum ‘hear’

I II III IV V VI VII

X

e e f g h h e

W

a b c c d d c

i i j j k l j

Y

m m n n o o g

Z

TABLE 4. Three types of principal-part analyses for a hypothetical system of conjugations Morphsyntactic property sets

Conjugations

Conjugations

I II III IV V VI VII

X

e e f g h h e

W

a b c c d d c

i i j j k l j

Y

m m n n o o g

Z

Morphsyntactic property sets

Static principal-part analysis {a, e, i} {b, e, i} {c, f, j} {c, g, j} {d, h, k} {d, h, l} {c, e, j}

Conjugations

I II III IV V VI VII

X

e e f g h h e

W

a b c c d d c

i i j j k l j

Y

m m n n o o g

Z

Morphsyntactic property sets

Adaptive principal-part analysis {a} {b} {c, f} {c, g} {d, k} {d, l} {c, e}

Conjugations

VII

VI

V

IV

III

II

I

X

e e f g h h e

W

a b c c d d c

i i j j k l j

Y

m m n n o o g

Z

Morphsyntactic property sets

Dynamic principal-part analysis {〈a, W〉} {〈b, W〉} {〈f, X〉} {〈g, X〉} {〈k, Y〉} {〈l, Y〉} {〈g, Z〉}

(1)

A viable set S of principal parts is OPTIMAL for some paradigm P iff there is no proper subset of S that is a viable set of principal parts for P.

A set S of principal parts is VIABLE for some paradigm P iff the members of S uniquely determine all of P’s members.

Some definitions:

C. Typological criteria distinguishing principal-part systems

Infinitive Imperative singular Imperative plural Perf. present Perf. recent past Perf. intermediate past Perf. remote past Perf. narrative past Imperf. near future Imperf. distant future Imperf. past continuous Imperf. past habitual Imperf. past conditional Subjunctive Nominalized stem1 Nominalized stem2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

TABLE 5. Twenty-six possible static principal-part analyses for Ngiti

Criterion A: How many principal parts are needed to determine a lexeme’s paradigm?

Number of dynamic Number principal parts Number of of static Average over conjugations principal all parts Maximum conjugations Kwerba (Trans-New Guinea; Irian Jaya) 4 1 1 1 Koasati (Muskogean; USA) 12 2 1 1 Gadaba (Dravidian; India) 4 3 2 1.25 Ngiti (Nilo-Saharan; DR Congo) 10 3 2 1.6 Fur (Nilo-Saharan; Sudan) 19 5 3 1.58 Comaltepec Chinantec (Oto-Manguean; 66 5 4 1.92 Mexico)

TABLE 6. Numbers of principal parts in the verb systems of six languages

Criterion B: Are the principal parts the same for all inflection classes?

This criterion distinguishes PARALLEL systems (in which distinct inflection classes possess parallel sets of dynamic principal parts) and SKEWED systems (in which there is no such parallelism among the dynamic principal parts of distinct inflection classes). By this criterion, all statically defined systems of principal parts are necessarily parallel; but this isn’t so for dynamically defined systems.

(2) Principal parts of Sanskrit verbs according to Lanman 1884 a. 3sg present indicative active b. … middle c. 3sg perfect active d. … middle e. 3sg aorist active f. … middle g. 3sg future active h. … middle i. Past passive participle j. Infinitive k. Absolute gerund form l. Conjunct gerund form

Present 3Pl Nonhuman

Perfect 3Pl Nonhuman

Subjunctive 3Pl Nonhuman

Present 3Sg

Perfect 3Sg

Subjunctive 3Sg

Present Non3

Perfect Non3

Subjunctive Non3

Conjugatio n

I,1a LH-o LH-ò LH-èl HH-o HH-ò HH-èl HH-òl HH-ùl HH-èl-à/-ì I,1b LH-o LH-ò LF-Ø HH-o HH-ò HF-Ø HH-òl HH-ùl HH-è I,1c LH-o LH-ò LH-ì HH-o HH-ò HH-ì HH-òl HH-ùl HH-è I,2a HH-ò HH-o HH-èl LL-o LL-ò LL-èl LL-òl LL-ùl LL-èl-à/-ì I,2b HH-ò HH-o HF-Ø LL-o LL-ò LL-Ø LL-òl LL-ùl LL-è I,2c HH-ò HH-o HH-ì LL-o LL-ò LL-ì LL-òl LL-ùl LL-è II,1a LH-i LH-i LH-itì HH-i HH-i HH-itì HH-i-A(l) HH-i-è HH-iti-A(l) II,1b LH-i LH-i LF-Ø HH-i HH-i HF-Ø HH-i-A(l) HH-i-è HH-è II,2a HH-ì HH-ì HH-itì LL-i LL-i LL-itì LL-i-A(l) LL-i-è LL-iti-A(l) II,2b HH-ì HH-ì HF-Ø LL-i LL-i LF-Ø LL-i-A(l) LL-i-è LL-è IIIa HH-ì HH-à HH-èl LH-ì LH-à LH-èl LH-è LH-e LH-èl-à IIIb HH-ò HH-ò HH-èl LH-ò LH-ò LH-èl LH-è LH-e LH-èl-à IIIc HH-ò HH-ò HH-èl LF-Ø LH-ò LH-èl LH-è LH-e LH-èl-à IIId HF-Ø HH-à HH-èl LF-Ø LH-à LH-èl LH-è LH-e LH-èl-à IIIe HF-Ø HH-à HH-èl LF-Ø LH-ò LH-èl LH-è LH-e LH-èl-à IVa HF-Ø HH-ò HH-èl LF-Ø LH-ò LH-èl LH-Al LH-e LH-èl-à IVb HH-ò HH-ò HH-èl LH-ò LH-ò LH-èl LH-Al LH-e LH-èl-à IVc HF-Ø HH-à HH-èl LF-Ø LH-à LH-èl LH-Al LH-e LH-èl-à IVd HH-à HH-à HH-èl LH-à LH-à LH-èl LH-Al LH-e LH-èl-à Shaded exponents indicate dynamic principal parts in one optimal analysis.

LH-ùl LH-ùl LH-ùl HH-ùl HH-ùl HH-ùl LH-i-è LH-i-è HH-i-è HH-i-è HH-e HH-e HH-e HH-e HH-e HH-e HH-e HH-e HH-e

HH-Al HH-Al HH-Al

Perfect 3Pl Human

LH-òl LH-òl LH-òl HH-òl HH-òl HH-òl LH-i-A(l) LH-i-A(l) HH-i-A(l) HH-i-A(l) HH-è HH-è HH-è HH-è HH-è HH-Al

Subjunctive 3Pl Human

TABLE 7. A dynamic principal-part analysis for Fur verbs

HH-èl-à HH-èl-à

HH-èl-à

LH-èl-à/-ì LH-è LH-è HH-èl-à/-ì HH-è HH-è LH-iti-A(l) LH-è HH-iti-A(l) HH-è HH-èl-à HH-èl-à HH-èl-à HH-èl-à HH-èl-à HH-èl-à

Present 3Pl Human

Criterion B: Are the principal parts the same for all inflection classes?

Kwerba Koasati

Yes (parallel) No (skewed)

1

Fur, Latin, Ngiti

Sanskrit

>1

TABLE 8. The intersection of Criteria A and B Criterion A: How many principal parts are needed to determine a lexeme’s paradigm?

Criterion C: How many principal parts are needed to determine a given word in a lexeme’s paradigm?

This criterion distinguishes SEGREGATED principal-part systems (in which each word in a lexeme’s paradigm is deducible from a single one of its principal parts) from INTEGRATED principal-part systems (in which at least some of a lexeme’s words must be deduced from a combination of its principal parts).

TABLE 9. Inferences from the principal parts in (2) Principal Inference parts (a) / (b) determine all active / middle present-system forms. (c) / (d) determine all active / middle perfect forms. (e) / (f) determine all active / middle aorist forms. (g) / (h) determine all active / middle future-system forms. (i) determines the past passive and past active participles. (j) specifies the infinitive form. (k) specifies the absolute gerund form. (l) specifies the conjunct gerund form.

HH-ò

HH-ò HH-à HH-à

HH-ò HH-ò HH-ò HH-ò HH-ò

HH-ò

HF-Ø HF-Ø HH-à

Present Non3 HH-èl HH-èl HH-èl

HH-èl

HH-èl HF-Ø HH-ì HH-èl HH-èl

Subjuncti ve 3Sg LF-Ø LF-Ø LH-à

LH-ò

LL-o LL-o LL-o LH-ò LF-Ø

Perfect 3Sg LH-ò LH-à LH-à

LH-ò

LL-ò LL-ò LL-ò LH-ò LH-ò LH-èl LH-èl LH-èl

LH-èl

LL-èl LL-Ø LL-ì LH-èl LH-èl LH-Al LH-Al LH-Al

LH-Al

LL-òl LL-òl LL-òl LH-è LH-è LH-e LH-e LH-e

LH-e

LL-ùl LL-ùl LL-ùl LH-e LH-e

Present 3Sg Subjuncti ve 3Pl Nonhuma nPerfect 3Pl Nonhuma

Perfect Non3

Conjugati on

LH-èl-à LH-èl-à LH-èl-à

LH-èl-à

LL-èl-à/-ì LL-è LL-è LH-èl-à LH-èl-à

HH-Al HH-Al HH-Al

HH-Al

HH-òl HH-òl HH-òl HH-è HH-è

HH-e HH-e HH-e

HH-e

HH-ùl HH-ùl HH-ùl HH-e HH-e

HH-èl-à HH-èl-à HH-èl-à

HH-èl-à

HH-èl-à/-ì HH-è HH-è HH-èl-à HH-èl-à

Shaded exponents indicate the dynamic principal parts of Conjugation IVb in the analysis given in Table 7.

HH-o HH-o HH-o HH-ò HH-ò

Subjuncti ve Non3

I,2a I,2b I,2c IIIb IIIc IVb IVa IVc IVd

Present 3Pl Nonhuma n Subjuncti ve 3Pl Human Perfect 3Pl Human

TABLE 10. Why two principal parts are needed to deduce the 3sg subjunctive form in Conjugation IVb in Fur Present 3Pl Human

TABLE 11. Degrees of integration in the principal-part systems of seven languages Average number of static principal parts required to deduce a word in a verbal paradigm Gadaba 0.67 Kwerba 0.75 Sanskrit, Koasati 1.00 Ngiti 1.07 Fur 1.11 Comaltepec 1.32 Chinantec

Criterion D: What is the morphological relation between a principal part and the nonprincipal parts that are deduced from it?

This criterion distinguishes MORPHOLOGICALLY COHERENT principal-part systems (in which each principal part shares its stem with the nonprincipal parts that are deduced from it) from systems that are MORPHOLOGICALLY INCOHERENT.

-rudhya

l.

3. Zero-grade form aruts-

gerunds of all compounds of rudh

--

1. Zero-grade form rundh- 2. Zero-grade form rurudh-

-rudhya

ruddhvā

--

stem of the past active participle

ruddhvā

roddhum

ruddha-

k.

middle aorist forms

roddhum

arauts- (3)

active aorist forms

j.

aruddha

f.

arauts-

case forms of the past passive participle;

arautsīt

e.

rurodh- (2) middle perfect forms

active perfect forms

ruddha

rurudhe

d.

rurodh-

i.

rurodha

c.

ruṇadh- (1) middle present-system forms

active present-system forms

are deducible from the principal part

future forms

runddhe

b.

ruṇadh-

Its stem

g, h. rotsyati, rotsyate rotsya-

ruṇaddhi

a.

Principal part

Other forms based on the same stem that

TABLE 12. The morphological coherence of the principal parts of Sanskrit rudh ‘obstruct’

Present 3Pl Nonhuman

Perfect 3Pl Nonhuman

Subjunctive 3Pl Nonhuman

Present 3Sg

Perfect 3Sg

Subjunctive 3Sg

Present Non3

Perfect Non3

Subjunctive Non3

Conjugatio n

I,1a LH-o LH-ò LH-èl HH-o HH-ò HH-èl HH-òl HH-ùl HH-èl-à/-ì I,1b LH-o LH-ò LF-Ø HH-o HH-ò HF-Ø HH-òl HH-ùl HH-è I,1c LH-o LH-ò LH-ì HH-o HH-ò HH-ì HH-òl HH-ùl HH-è I,2a HH-ò HH-o HH-èl LL-o LL-ò LL-èl LL-òl LL-ùl LL-èl-à/-ì I,2b HH-ò HH-o HF-Ø LL-o LL-ò LL-Ø LL-òl LL-ùl LL-è I,2c HH-ò HH-o HH-ì LL-o LL-ò LL-ì LL-òl LL-ùl LL-è II,1a LH-i LH-i LH-itì HH-i HH-i HH-itì HH-i-A(l) HH-i-è HH-iti-A(l) II,1b LH-i LH-i LF-Ø HH-i HH-i HF-Ø HH-i-A(l) HH-i-è HH-è II,2a HH-ì HH-ì HH-itì LL-i LL-i LL-itì LL-i-A(l) LL-i-è LL-iti-A(l) II,2b HH-ì HH-ì HF-Ø LL-i LL-i LF-Ø LL-i-A(l) LL-i-è LL-è IIIa HH-ì HH-à HH-èl LH-ì LH-à LH-èl LH-è LH-e LH-èl-à IIIb HH-ò HH-ò HH-èl LH-ò LH-ò LH-èl LH-è LH-e LH-èl-à IIIc HH-ò HH-ò HH-èl LF-Ø LH-ò LH-èl LH-è LH-e LH-èl-à IIId HF-Ø HH-à HH-èl LF-Ø LH-à LH-èl LH-è LH-e LH-èl-à IIIe HF-Ø HH-à HH-èl LF-Ø LH-ò LH-èl LH-è LH-e LH-èl-à IVa HF-Ø HH-ò HH-èl LF-Ø LH-ò LH-èl LH-Al LH-e LH-èl-à IVb HH-ò HH-ò HH-èl LH-ò LH-ò LH-èl LH-Al LH-e LH-èl-à IVc HF-Ø HH-à HH-èl LF-Ø LH-à LH-èl LH-Al LH-e LH-èl-à IVd HH-à HH-à HH-èl LH-à LH-à LH-èl LH-Al LH-e LH-èl-à Shaded exponents indicate dynamic principal parts in one optimal analysis.

LH-ùl LH-ùl LH-ùl HH-ùl HH-ùl HH-ùl LH-i-è LH-i-è HH-i-è HH-i-è HH-e HH-e HH-e HH-e HH-e HH-e HH-e HH-e HH-e

HH-Al HH-Al HH-Al

Perfect 3Pl Human

LH-òl LH-òl LH-òl HH-òl HH-òl HH-òl LH-i-A(l) LH-i-A(l) HH-i-A(l) HH-i-A(l) HH-è HH-è HH-è HH-è HH-è HH-Al

Subjunctive 3Pl Human

TABLE 7. A dynamic principal-part analysis for Fur verbs

HH-èl-à HH-èl-à

HH-èl-à

LH-èl-à/-ì LH-è LH-è HH-èl-à/-ì HH-è HH-è LH-iti-A(l) LH-è HH-iti-A(l) HH-è HH-èl-à HH-èl-à HH-èl-à HH-èl-à HH-èl-à HH-èl-à

Present 3Pl Human

TABLE 13. The intersection of Criteria C and D Criterion C: How many principal parts are needed to determine a given word in a lexeme’s paradigm? 1 >1 (segregated) (integrated) Koasati, Criterion D: What is coherent Latin Kwerba, the morphological Sanskrit relation between a principal part and the nonprincipal parts that incoherent Fur, Ngiti are deduced from it?

Criterion E: Are corresponding words in distinct paradigms determined by the same principal parts?

This criterion distinguishes ISOMORPHIC principal-part systems (in which a lexeme’s nonprincipal parts are inferred from its principal parts in the same way from one inflection class to another) from NON-ISOMORPHIC systems.

TABLE 9. Inferences from the principal parts in Table 9 Principal Inference parts (a) / (b) determine all active / middle present-system forms. (c) / (d) determine all active / middle perfect forms. (e) / (f) determine all active / middle aorist forms. (g) / (h) determine all active / middle future-system forms. (i) determines the past passive and past active participles. (j) specifies the infinitive form. (k) specifies the absolute gerund form. (l) specifies the conjunct gerund form.

TABLE 14. Deducing a Latin verb’s present active participle from its dynamic principal parts Conjugation 1st 3rd 3rd (-iō) 4th 1sg present indicative dūcō capiō audiō (2) laudō (1) active ↓ ↓ ↓ Present active laudant- dūcent- capient- audientparticiple ↑ ↑ Present active audīre laudāre (1) dūcere capere infinitive

TABLE 15. The intersection of Criteria B and E Criterion B: Are the principal parts the same for all inflection classes? Yes No (parallel) (skewed) Criterion E: Are Yes Kwerba, corresponding words (isomorphic) Sanskrit in distinct paradigms Fur, Koasati, No (nondetermined by the Latin, Ngiti same principal parts? isomorphic)

D. Conclusion

(3) Summary of typological criteria Criterion A: How many principal parts are needed to determine a lexeme’s paradigm? Criterion B: Are the principal parts the same for all inflection classes [if a dynamic system of principal parts is assumed]? Criterion C: How many principal parts are needed to determine a given word in a lexeme’s paradigm? Criterion D: What is the morphological relation between a principal part and the nonprincipal parts that are deduced from it? Criterion E: Are corresponding words in distinct paradigms determined by the same principal parts?

Logically, no principal-part system can be both skewed and isomorphic, nor can any have a single principal part and (a) be integrated rather than segregated or (b) be parallel and nonisomorphic.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12 13 14 15 16

1 1 1 1 >1 >1 >1 >1 >1 >1 >1 >1 >1 >1 >1 >1

A

TABLE 16. Logically possible types of principal-part systems Observed B C D E examples parallel segregated coherent isomorphic Kwerba parallel segregated incoherent isomorphic skewed segregated coherent non-isomorphic Koasati skewed segregated incoherent non-isomorphic parallel segregated coherent isomorphic Sanskrit parallel segregated coherent non-isomorphic parallel segregated incoherent isomorphic parallel segregated incoherent non-isomorphic parallel integrated coherent isomorphic parallel integrated coherent non-isomorphic parallel integrated incoherent isomorphic parallel integrated incoherent non-isomorphic skewed segregated coherent non-isomorphic skewed segregated incoherent non-isomorphic skewed integrated coherent non-isomorphic Latin skewed integrated incoherent non-isomorphic Gadaba, Fur, Ngiti, Comaltepec Chinantec

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Finkel, Raphael & Gregory Stump. 2006. Principal parts and morphological typology. Technical Report No. 459-06, Department of Computer Science, University of Kentucky. To appear in Morphology.

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References